An oil light is only designed to come on when the engine oil pressure is too low.
And adding too much oil would not cause the engine oil pressure to drop so your engine oil light should not come on when you overfill your engine oil.
If your oil light is coming on your engine oil pressure is likely getting low which could be caused by a clogged oil filter, bearing clearances being too much due to worn bearings etc.
I would get the car checked out if your engine is full of oil but the oil light is still coming on as it shouldn't come on unless the oil pressure is too low.
But if you did overfill the engine will too much oil as in you overfilled the engine oil with a quart or a 1/2 quart too much then you need to drain the excess oil.
If the oil is just overfilled but an inch above the full level then it should be okay.